Difficulty: Easy
Correct Answer: 9.6%
Explanation:
Introduction / Context:
This basic simple interest question gives you the principal, the interest earned, and the investment period in months. You must determine the equivalent annual rate of simple interest.
Given Data / Assumptions:
Concept / Approach:
Convert the time from months to years, then use the formula SI = (P * R * T) / 100 to solve for R. Carefully handle the fraction of a year when converting 3 months into years.
Step-by-Step Solution:
Step 1: Convert the time: 3 months = 3 / 12 = 1 / 4 year.
Step 2: Write the simple interest formula: SI = (P * R * T) / 100.
Step 3: Substitute SI = 18, P = 750, and T = 1 / 4.
Step 4: The equation becomes 18 = (750 * R * (1 / 4)) / 100.
Step 5: Simplify the fraction: 750 * (1 / 4) = 187.5.
Step 6: The equation is now 18 = (187.5 * R) / 100.
Step 7: Multiply both sides by 100: 18 * 100 = 187.5 * R.
Step 8: So 1800 = 187.5 * R, giving R = 1800 / 187.5 = 9.6% per annum.
Verification / Alternative check:
Verify by recomputing the interest with R = 9.6%. SI = (750 * 9.6 * 1 / 4) / 100. First compute 750 * 9.6 = 7200. Then 7200 * 1 / 4 = 1800. Finally, 1800 / 100 = 18, which matches the given interest, so the rate is correct.
Why Other Options Are Wrong:
2.4%, 7.2%, and 12% all produce interest values different from Rs. 18 when the same principal and time are used, so they are inconsistent with the given data.
Common Pitfalls:
Students often forget to convert the time from months to years properly, or they mistakenly use 3 years instead of 3 months in the formula. Another common error is to misplace the 100 in the denominator, which leads to incorrect computation of the rate.
Final Answer:
The simple annual interest rate is 9.6%.
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